Computation of the Linear and Nonlinear Stability of a Two-Layer Couette Flow

This work considers the linear and nonlinear stability of a two-layer Couette flow in a horizontal channel. At the first stage, the Navier-Stokes equations are linearized in both phases. We then solve the spectral problem and investigate the dynamics of periodic disturbances in a wide range of changes in the volumetric content of liquids and the velocity of the top plate. Both the neutral and the fastest growing disturbances of the unstable interface mode are calculated. At the second stage, nonlinear stationary traveling wave regimes were calculated for the Couette flow in a horizontal channel using the complete Navier-Stokes equations for both liquids. The results are compared to the experimental data available in the literature.